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On the Action of the Dual Group on the Cohomology of Perverse Sheaves on the Affine Grassmannian

Published online by Cambridge University Press:  04 December 2007

E. Vasserot
E. Vasserot
Affiliation:
Département de Mathématiques, Université de Cergy-Pontoise, 2 Av. A. Chauvin, 95302 Cergy-Pontoise Cedex, France. E-mail: eric.vasserot@u-cergy.fr
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Abstract

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It was proved by Ginzburg, Mirkovic and Vilonen that the G(O)-equivariant perverse sheaves on the affine Grassmannian of a connected reductive group G form a tensor category equivalent to the tensor category of finite dimensional representations of the dual group G∧. In this paper we construct explicitly the action of G∧ on the global cohomology of a perverse sheaf.

Keywords

perverse sheavestensor categoriesLanglands duality
Type
Research Article
Information
Compositio Mathematica , Volume 131 , Issue 1 , March 2002 , pp. 51 - 60
Copyright
© 2002 Kluwer Academic Publishers